## 9.2 Appendix 2 - Newton's Inverse Square Law

# Newton's Inverse Square Law -

**Distance** is an important factor when considering **application** **specific detectors**. How close can you get the detector to the **target radiation source**. **Worker safety** and **ALARA** (as low as reasonably achievable) requirements, for example, emphasize the **greatest distance** from the source whenever possible. Perhaps you need a **larger crystal**...let's explore.

The Inverse Square Law shows an **exponential increase **in dose as you **move closer **to the source. It states:

Anypoint sourcewhich spreads its fluence equally inall directionswithout a limit to its range will obey theinverse square law.

This comes from strictly **geometrical considerations**. The intensity of the fluence at any given **radius (r)** is the source strength divided by the **area of the sphere**. Being strictly **geometric in its origin**, the **inverse square law** applies to diverse phenomena.

Point sources that obey the inverse square law include:

**Gravitational force****Electric field****Light****Sound****Radiation**

As one of the fields which obey the general **inverse square law**, a **radiation point source** can be characterized by the diagram below whether you are talking about **Roentgens, rads, sieverts [1] or rems**. All measures of exposure will drop off by the inverse square law. For example, if the radiation exposure is **100 mR/hr at 1 inch** from a source, the exposure will be **0.01 mR/hr at 100 inches**.

Notice that the diagram below only **illustrates the principle of the inverse square law**. In practice the radiation from a **point source** is **spherical (4π)**. Therefore, when this relationship is applied to a real application the detector must be in the shape of a **right circular cylinder **and the **source **should be positioned directly in **front of the detector **(on a centerline with the detector to avoid errors in geometry). In addition, **measurement errors** in **exposure (dose rate)** must be minimized by positioning the **radioactive source **no closer than **five times the diameter of the detector**. This is because all photons impinging on the detector are not completely absorbed if the **solid angle is too large**.

Be aware that some **detectors **have **shapes **that **don’t conform **to the **inverse square law **when it comes to **accurate dose rate measurements**. For example, a detector measuring **4"x4"x16" **cannot accurately **absorb all photons **in a solid angle from a source at any position from this detector. For these **non-traditional detectors **the factory calibration is usually set for compliance with **NORM background**.

**[1] **The **sievert **is the SI (International Unit) of exposure and is **equal to 100rem**.